1. Field of the Invention
The invention relates to opacifying extenders more particularly, to sulfur particle opacifying extenders for polymers and polymer coatings derived from water-borne emulsions.
2. Description of the Prior Art
A currently used opacifying extender for coating, water-borne emulsion compositions and the like is comprised of spherical particles consisting of a polymer shell surrounding an inner air bubble which typically has an outer diameter of about 0.4 .mu.m and a core diameter of about 0.27 .mu.m. Such an extender is produced by Rohm and Haas under the product name ROPAQUE.TM..
The opacity of such extender particles can be calculated by modeling them as spherical air bubbles, having a refractive index of 1.0 dispersed in a polymer matrix with refractive index of approximately 1.55. The results are shown in FIG. 1. A maximum opacity of about 0.015 .mu.m.sup.-1 for the matrix containing the extender is achieved for particles having a diameter of approximately 0.2 .mu.m.
This model relates opacity of particles dispersed in a matrix to particle diameter, particle refractive index and matrix refractive index and can be applied to generate contours of constant opacity as a function of opacifying extender particle diameter and refractive index for spherical particles dispersed in a polymer matrix having a fixed refractive index of 1.55. The results of such calculations, as shown in FIG. 2, indicate that particles having a refractive index approximately equal to about 2.0 and a particle diameter in the range of from about 0.05 to about 1.00 .mu.m exhibit an opacity of about 0.015 .mu.m.sup.-1 when included in a matrix of refractive index 1.55, such as the polymer film which remains when the water of a water-based paint emulsion evaporates, an opacity comparable to commercially available microvoid extenders. Opacity is defined by the relationship O.sub.p =1/f*h* wherein f* and h* respectively represent the total particle volume per unit volume of film and the film thickness for which the luminous reflectance, R.sub.1um, has a value of 0.98 which represents a luminous reflectance indistinguishable to the human eye from the luminous reflectance of an infinitely thick suspension of non-absorbing particles having an R.sub.1um of one. The luminous reflectance over a range of wavelengths .lambda..sub.1 to .lambda..sub.2 depends upon r, the particle radius; n.sub.p, the particle refractive index (no absorption assumed) and n.sub.m, the refractive index of the medium as given by the following equations ##EQU1## wherein I(.lambda.) is the special irradiance, K(.lambda.) is the luminous efficiency of the eye using simple two-stream radiative transfer theory, and R is the monochromatic reflectance given by equation (2). The scattering coefficient s is given by: ##EQU2## wherein the terms ##EQU3## and g are the scattering cross section per unit particle volume and mean cosine of the scattering angle, respectively, as calculated by a computer program given in Appendix A of "Absorption and Scattering of Light by Small Particles", C. F Bohren and D. R. Huffman, John Wiley and Sons, New York, 1983, the content of which is herein incorporated by reference.
While the currently used opacifying extenders can successfully achieve desired results, they are generally expensive and require close particle size control to retain the required opacity. Thus, there is a need for a relatively less expensive opacifying extender requiring less rigorous particle size control.